Suppose a representative agent with preferences
U(c0, ec1) = u(c0) + ßEu(ec1)
where ct
is the per-capita consumption at date t = 0, 1, where u is increasing and
concave, and 0
access to a saving/borrowing technology with gross interest R such that c0 = z0 -s,
c1 = z1 + sR.
(a) Suppose first that there is no growth and no uncertainty z0 = 1 and z1 = 1.
Determine the market-clearing interest R.
(b) Now the government engages in reforms which imply that GDP grows to ze1 =
z0(1 + ge) with E(ge) > 0. A journalist claims that this boom must increase
interest rates. Comment (in three sentences or less).
2. Consider a country H which is populated by 2 identical individuals. They are
identical in their endowment ?H = (?Ha, ?Hb) = (1, 2), where the state of the world
s ? {a, b} captures uncertainty and Pr(a) = 0.5 = Pr(b). Their utility functions are
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PS2 Financial Economics 1. Suppose a representative agent with preferences U(c0; ec1) = u(c0) + Eu(ec1) where ct is the per-capita consumption at date t = 0; 1, where u is increasing and concave, and 0 <> 0. A journalist claims that this boom must increase interest rates. Comment (in three sentences or less). 2. Consider a country H which is populated by 2 identical individuals. They are identical in their endowment !H = (!Ha; !Hb) = (1; 2), where the state of the world s 2 fa; bg captures uncertainty and Pr(a) = 0:5 = Pr(b). Their utility functions are uH(x) = ??exp(??x): (a) Suppose competitive and complete markets for Arrow-Debreu (A-D) securities. Determine the equilibrium prices for A-D securities. (b) The neighboring country N is populated by 4 identical individuals. They are identical in their endowment !N = (!Na; !Nb) = (1; 0:5) and their utility functions are uN(x) = ??0:5 exp(??2x): States s 2 fa; bg are perfectly correlated across countries, i.e. a obtains in economy H if and only if it also obtains in economy N. Suppose that the countries agree to unify into a big integrated economy NH. The two groups of agents 1 and 2 are now able to trade on complete and competitive markets for A-D securities. Determine equilibrium prices in the unied economy NH. 3. Use your knowledge about stochastic dominance to compare two random variables ex; ey. Let ex (2; 12 ; 5; 12 ) (equal probabilities of getting 2 or 5). Find the values of p 0 for which the following statement is true: Every expected utility maximizer with increasing von Neumann-Morgenstern utility function prefers ey (2; 14 ; 3; p; 6; 34 ??...